Fluid flow pulsation damping



June 11, 1957 s. E. lsAKox-F FLUID FLOW PULSATION DAMPING 2 Sheets-Sheet 1 v Filed Aug. 13, 1953 ATTORNEY June 11, 1957 s. E. lsAKoFF FLUID FLow PULsATIoN DAMPING Filed Aug. 13', 1953 TRANSMISSIN 2 She'tts-Sheet 2 I l l I l I l l l l I 1.0 I' y FREQ UENCY RAT/0 INVENTOR shezdmlsajfzj ATTORNEY 2,795,374 fFLUrD FLOW PULsArroN DAMPING Sli'eldon E. IsakoiBWilmington; Del., assignor tofE. I.v du

2,795,374 lPatenteelfJune #1 1 1957 ice 2 aprovidedL-and contained all in a singletankor shell, which at` the Vsame vtime houses `the interconnectingy pipe communicating with eachofthe compartments.

-.Itwill be understood that other embodiments will be- 5 fcome-apparenefrom'- the foregoing-:that may fall within Pont de vNemoursi-and Company, Wilmington,-Del.,ga

corporation of Delaware Applicarion=August 13; 19ss,`sena1N0. 373,969

lfz claims. .'(cl'. 23o- 236) Thisinvention relates to means'for damping'orreducf15 ing the flow and pressure pulsations' in gas streams,- such as those'that exist at'the suction and discharge points of reciprocating compressors, blowers, internal combustion engines, and the like.

the broad principles Tofthe inventionherein set forth and fdisclosed. alt isftobe-understoodthat--the'specific form of'this f invention as it--rnay`y be applied in any given circumstance lernayvdepend upon fthefsource Aof the pulsations` where Numerous means and methods are known commercia11y-20in WhChI for damping pulsations, but in most part are suitable only for certain conditions for which they were specifically designed or applied, and are ineffective, uneconom'ic'al, "or 'inapplicable generally' to widely varying' conditions Y"such as' are encountered in high-pressure 'chemical'4 25 fOIm 0fill'fefcommuncafllgPipes; operations.

`Major `advantages that are atv once apparent fronifthe present invention as applied in actual operationsinclude increased pulsation reduction and simplicity"'of construcinclude (l) 'excessive mechanicalV vibration, resulting'in i unsafe'conditions-and fatigue failures; (2) excessiveipfres- "sure-stresses; (3 )'ditii'cult process control; j'(4)"'varible pressor or pump efficiency.

il"It has'tlbeenfdetrmined that"when" the 'single""r'rieans provided by Ithis invention is included in the t'iidorgas stream, pressure and tlowsuctuations are at once sharply tion,v and'particularly -the' ability' 'by'this 'meansof 'pre-"30 "FH 1E-ig. 1- isfalongitndinal,sectional` View `offone embodiment of a unit constructed in, accordance-withthe present invention, vand Fig. 2 is aviewsimilar to 'FigL l but showing a modified Fig.V 3`is a crosssection'fthrough another embodiment, while Eig: 4 represents a still further..embodiment,y and lliig.f5-is a.igraphicaillustrationofnthe performance of affunitwoonstructed in= accordancewith this invention.

ig: :19A designatesthesource ofipulsatingf` ow, v'which-sinsthe broadaspects-Iofthe invention may be any one of tdifferentgasmoving units-'imparting pulsations to a fluid stream in pipe B. a The uid pulsation sources may include any of the usual piston-type compressorsA 'ernv 35 ployed in gas compressor or chemical plants. Such com* 40 time.

reduced. One theoretical?` feature of the present inven-k tion comprises applying the principles of wave interferi ence;y byt ifoperatingu-the f components fof :the waveftlrain'in the gas streamffinsch armanner-thatt'hey tend-'to cancel ment'y of thetanks' andg interconnecting passage assembled ima-conformity withE the principles f' and -for'mnlaeffu'lly Aediiscus'sed hereinafter, itfwill at once be apparent thatlmuch greater pulsation reduction is attained than canbeproduced with priorx-known single tank; or 'evenf two-compartrnent tanks having' thesame total volume' andfentailing Vfappijtnrimately,.the'samepressuredrop. In a preferred embodiment of the invention three compartments are pressors maylbewsingleor -lmultiacylinder and may be in'glefforlfdouble acting. 1A' given -compressor willproduce'pusatio'nsLinathel-passage`conneetedto it at a rate corresponding to the number of gas discharges per unit The fundamental-frequency of pulsation F in cycles per second is given by:

'twhere'-n1^-is"the number of cylindersfor a single-acting "*machinefortwicethe number of` cylinders for a doubleacting compressor. The gas is discharged by the 'compressor through lthepulsation damper when the pulsa- Ltions are to be reduced ori thefdischarge side of the prime mover. If the pulsations are to removed on the. inlet side of the primemover, the-apparatus should belocated onthat side. "It'will'be, understood also V`that the exact location'r of 'the pulsation damper will depend-on` the 5 lpurpose for' its operation,. space requirements,- and other conveniencefactors.

As' shown in Fig. 1, the` damper comprises asingle shell, C, with two transverse partitions, D and E, divid- ,fingtheishell intothree chambers orzones," F, lG, and

-fThechambers'orvzones provide capacitance where Qffgaslrushing infis compressed and stored vfor short periods wofftime. `Gasenters' the lunit at I and-discharges at I. y'Thesefinletand' discharge points-merely 'represent con- :tsnections'lto-Land from chambers F and-H, and are not 'ne'cessarilyrequired tobe in' line as shown.' Since the construction is substantiallyy symmetrical,I :the direction #fof gas ow-throughthedevice is immaterial. l .As shown, lfitheshellIcontains apipe Kinterconnecting-l the three @chambers-for zones. f The mass ofgas `in 'the pipe K fipossessesiriertiaand resists achange in its vrate ofow;

7Qipipeo K therefore lrepresents Yan inductive-- passage.

Chamberbor lz'one G islfully'. closedlexce'p't'f 1the t opening into the interconnecting pipe L, which pipe also namic properties of the gas.

constitutes an inductive passage. The pipe L opening to chamber or zone G is connected as shown substantially at the midpoint of pipe K.` Gas therefore moves in and out of this chamber as with a side-branched surge tank. The volumes of the chambers and the length and diameter of the interconnecting pipe are predetermined in a manner explained more fully hereinafter. The pipe K is preferably welded to and supported by the shell andtransverse partitions. Liquid `which may separate out in the apparatus is removed `from the chambers through the drain plugs M, N, and O.

While the intermediate chamber or zone may be `of substantially the same capacity `as theinlet `and outlet chambers or zones, the volume or capacityof the central or intermediate chamber or zone may vary between 60% and 160% of the volume or capacity 0f the inlet `and outlet chambers or zones.

A. Method of determining Size of chambers and interconnecting pipe 1. Determine the lowest frequency of pulsation `which one desires` to eliminate. As described earlier, when the source of pulsation is a reciprocatingcompressor, this frequency is given by Equation l. All harmonics of this fundamental frequency will be higher than this,

of course. Where the source of `pulsation is a rotary blower, the lowest frequency of pulsation is given by (2)` Fgnz-P- M- where n., is the number of blower blades.

2. Select the cut-off frequency, fc, of the pulsation damper at 80-90% of F. (Nora- The smaller the ratio the more conservative will be the design. Values of fc/F greater than 1.0 will not give as high a degree of pulsation damping as below 1.0.)

3. Determine the volume of the chambers and the lengths and diameters of the internal passage by the following relationship:

LlV :.0398c (3) dill-l-P) fs' where: V=volume of chambers F and H, cu. ft. L1=length of interconnecting pipe `from x to y, ft. r11-:diameter of interconnecting pipe between x and y, ft. c=velocity of sound in gas, ft./sec. p--a numerical factor which can be set between 0.3 and .08, preferably 0.45 to 0.65.

The velocity of sound in the gas may be approximated from tables, and corrected for the temperature and pressure conditions which exist in the line where pulsations are to be reduced,or determined from the thermody- (A discussion onthe computation of the velocity of sound in a gas is given in various sources, including Vibration and Sound," by P. M. Morse, 2nd edition, pp. 217-221, 1948.)

The right hand side of Equation 3, involving the cutolf frequency and the properties of the gas, has now been specified, `and a numerical value can be computed.

Consider now the left side of Equation 3. The numerical value of p is set first. A value of` 0.55

l is usually convenient and leads tohighly eective de- La d,2 is set, depending upon whether the allowable pulsation damper volume or the fluid ow pressure loss through the unit is considered to be the limiting factor. In high pressure applications, the cost of heavy-walled vessels may determine or govern the design to be based on a minimum volume basis, while considerable pressure loss may be allowable. On the other hand, at low pressures, material cost might be a relatively small percentage of the total installation cost, but pressure drop can well be the critical factor.

(a) If total volume is the limiting factor, the design would proceed as follows: Set the volume, V, equal to approximately 20-30 times the volume of a single flow pulse from the prime mover. That is, the volume V, is given by:`

Where Q `equals the average flow rate in cubic feet per second, and F is the fundamental pulsation frequency in cycles per second. Where the pressure of a gas being handled is high enough to reduce its compressibility (increase the velocity of sound in the gas), the above multiplication factor should be increased to compensate for the reduction. That is, if the gas compressibility is reduced by a factor of two, then Formula 4 should read This is to prevent excessive pressure pulsations being reflected back to the prime mover. With V specified, the ratio isestablished. The length and diameter are then chosen for convenience. For the design formulae to be accurate, it is important to keep the length of the interconnecting pipe below 1/2 wave length of sound in the gas. Experience indicates that in the gas handling held, the length of the interconnecting pipe need seldom exceed 1A: of the fundamental wave length.

(b) Where the pressure drop` is the limiting factor,

the ratio is arbitrarily set at as large a value as can be tolerated with regard to the pressure loss. Pressure drop through the chambers and interconnecting pipe is computed in the usual manner, based on the average gas flow rate through the unit. ln setting the values of L1 and d a convenient starting point is to set the value of d1. The pressure drop through the unit is approximately equal to (L5-iii?) velocity heads (Using the velocity head concept in pressure drop calculations, C. E. Lapple, Heating, Piping and Air Conditioning, vol. 17, pp. 179-83, 262-67, 319- 24, 1945) based upon the velocity in the interconnecting pipe. (Now, the value of V can be determined since all other terms in Equation 3 `havepreviously beendetermined.)

(c) Where neither total volume or pressure drop are specified, anel'fective, economical unit can usually be designed by starting with the interconnecting pipe and pipe lin'e diameter.

4. It remains only Lto 4-deterniine 4the volume of the center chamber,` and '-the length -and diameter of `the passage leading from.point.Z and connecting to chamber G.

The volume of G she'uldbe set' equal to 2pV. Since p and V have already been determined, the voliief chamber VG- can 1vbe computedlnumerically. i 'The Xlength,

L2, -and diameter, d' `ofy thetpipe lLf-.leading4 from point Z valuesof al2 `as low as 1/5 VVof d1. 'Iff-thetratio gofydz/al1r is less than 0.2, vthe/revensistanceftouidmotion ofi pipe- -Lrfwill be high, and the eiectiveness of the capacitancefcham- .ber Gwill be decreased; 'dacould bemadeggreaterthn d1, v.but rthis wouldf not be-.economical, since sthe il'ength `La would'then have to be increased in orderzto=obtain a specified numerical value of z '..d'

required by Equation l5. I

Although the'degree of `pul'sa'tion reduction that is achieved in practice vby means ofi asin'gle, three-compartment combination as illustratedhereidwill, Ain'g`e'r`1"e'ral,

Abe entirely "adequate, it .will be apparent from the fiore- :going that teven greater .pulsation *.damping Will be Iobtainedbywincluding or.. providing additional compartments -with their associated interconnecting' pipes designed in -fconformity vvi/ith theprecedingprincipls and formulae.

The additional chambers and interconnecting Lpipes may fbefpla-c'ed inthe .gasstream following L--tlie three-'chamber unit, and again, forsome.purposes,-al1-compartments and pipes may be placed in a single shell. y

`It should `be-understood-that''equivalent values forv the inductive passages determined as specified above could be obtained by using two or more interconnecting pipes in parallel. The effective inductance of n pipes of equal length in parallel arrangement is equal to of a single section of such pipe. Thus, if a number, n, of parallel inductive passages were used, the length of each passage would have to be n times that of the single passage specifi-ed in the preferred method of design above. Clearly, this is not economical, and has no apparent advantages over the single inductive passage.

It should further be understood that equivalent values for each of the capacitive chambers determined as specified above could be obtained by providing more than one compartment or tank in parallel arrangement. The effective capacitance of n chambers of equal volume in parallel arrangement is equal to n times the capacitance of a single such chamber. Thus, if a number, n, of parallel capacitance chambers were provided, the volume of each chamber would have to be times that of the single chamber or compartment specified in the preferred method above. In general, it will be found more economical to provide or employ a single capacitive chamber.

It will be understood, and the claims are to be so yconstrue'd, "that :the `stated -equations texpress 'the 4tlie- -oreticallyey correct lrelationships l`and vvalues fand that :1in .practice it-fmaynotbe` necessary" to adhere precisely there- 'to 'f so long as the i calculations or T1 relative z proportions of lthe apparatus cnfom fundamentally. and substantially ato the equations. y

A further modification lof "the Athree-compartmented pulsatintdamperisillustrated in Figure"'4 iniwhich the corresponding center or `intermediate compartment, G1, comprises the annular space betweenfthe'outerandinner -shells C1 andC,respective`ly,1as shown, the=remaining -zquivalent' elements tol those illustratedfin 4Figures f1 -to -3 -beingfsimilarly designated.

B. ExampleA -To .further illustrate the method of design and .practical *application 4of the invention, the v`following example is v selected from anactual installation.

Problem: =To remove pulsations from agas stream, .substantially ethylene, 'discharging from a` double 'acting acompressor intoa=6in.fline. The minimumcompresso'r v'operating rspeed .is2'50 y'R.'P. M., maximumf3'00"R.P."Mf 'and `themairimum -iiowrate is 8,200 `pounds per ho'ur. fLineqpressure at-'thedischarge is 425 p. s. i., temperature 100 C., lfdensity 1.81 lb./cu. \ft., yand Athe velocity lof `.sound in the "gas `mixture :at 'these conditions 'is `115,0 'ft/sec. It-*is further specied that spaceislimitedian'd lthat-the 'volume' of damper shouldbe kept' to a minimum.

JSolution: `/Minimum fundamentalfrequency =8.33 pulses/sec.

'300 .Maximum-pulsation frequency=36 C11. ft.

[Set the volume ofthe inlet chamber equal to-20 times the volume of'theflow pulse, and set the value of p Yequal to' 0.55. Set fc at 85 %.of minimum fundamental frequency.

iVolume ,per pulse:

Volume ofrinlet chamber=volur`ne 'of Y exit :chamber -=420(o.1'26)=^2.52 cu; ft. VVolume'r of z center chamber='2(0.55) (2.'52)=278 cu.c ft. jc=.85(8.33)=7.08 cycles/sec.

From Equation 3 .0398(1150)2(1+0.55) c112- 2.52(7.08)2 From computation of the fluid pressure drop for the maximum gas iiow rate, it was determined that an interconnecting pipe whose nominal inside diameter was 2 inches would be satisfactory. Thus, the length, L1, of the interconnecting pipe, K (or the distance xy), is:

(Actual inside diameter of a 2-inch schedule 40 pipe is 2.067 in.) The length to the T in the interconnecting pipe, xz=1/z (19.2) :9.60 ft. Using a 2-inch pipe also for the passage leading to the center chamber, G, the length L2 or the distance zz' is given by Equation 6:

Figure presents a generalized plot of pressure pulsation -transmission versus pulsation frequency performance of pressed as a fraction of the cut-off frequency of the pulsa-` tion damper. Recalling that in the design of embodiments of the invention, fc is chosenat 80-90% of the lowest frequency of pulsation to be eliminated (F), it will be apparent that in any installation, operation will always be to the right of the dotted line, and pulsations will be substantially eliminated.

To indicate the remarkable effectiveness of the invention in damping fluid pulsations, measurements made before and after installation of the unit given in the example above will be given. Before installation, the maximum amplitude of pressure pulsations in the ethylene line was 40 p. s. i. or approximately 10% of the average line pressure. After installation, with the compressor operated at 275 R. P. M., the amplitude of pressure pulsations downstream of the damper was 1.0 p. s. i., a reduction to less than 0.25% of line pressure.` In addition, the amplitude of pressure pulsations between the damper and the compressor was only 21.1 p. s. i. Installation `of the damper thus achieved two desirable results:`

reduction of pulsation at the compressor discharge and substantially complete elimination of pulsation in the ethylene process line. The measured value of the pulsa-` tion transmission ratiol was 0.047, whereas the predicted value of this ratio (Figure 5) was 0.030, thus indicating another advantage of the invention in that the results can be closely predicted.

I claim:

1. In combination with a gas compressor or blower, apparatus for dampening pulsations in a gas stream hav ing pulsating ow delivered by said gas compressor or blower comprising separate gas entrance and gas exit chambers having relatively large eapaoitances, said gas entrance chamber communicating with said gas compressor or blower and said gas exit chamber communicating with agas delivery line, a third capacitance chamber, and an inductive passage or conduit in open communication with said gas entrance and gas exit chambers, said inductive` passage being provided with a branch pas sage of substantial inductance .in open communication with said third capacitance chamber, the volumes of said 4 chambers and the dimensions of said inductive passage .8 1 t and said branch passage having predetermined values substantially in accordance with the following equations:

LIV 03981:2 i 12(1-1-12) f.2 and L11-@L1 (if-411ml? `where:`

L1=1ength in feet of the inductive passage in open communication with said gasentrance and gas exit chambers,

d1=diameter in feet of said inductive passage,

V=volume in cubic feet of each of said gas entrance and exit chambers,

p=a numerical factor which canbe assigned a value in the range 0.3-0.8, but preferably OAS-0.65,

c=the velocity `in ft./sec. of sound in the gas, and

fc=a selected cut-olf frequency in cycles/sec. above which pulsation dampening is `desired and where 2pV=volume in cubic feet ofsaid third capacitance` chamber,

L,=length in feet of said branch passage connecting said inductive passage with said third capacitance chamber, and

d2=diameter in feet of said branch passage connecting said inductive `passage `with said third capacitance chamber.

2. An apparatus according to claim 1 wherein fc is of a preselected value below the lowest frequency of pulsation imparted to said gas stream by said compressor.

References Cited in the le of this patent UNITED STATES PATENTS 2,297,046 Bourne Sept. 29, 1942 2,343,152 Marx Feb. 29, 1944 2,405,100 Stephens July 30, 1946 2,437,446 i Stephens Mar. 9, 1948 2,474,553 Stephens June 28, 1949 2,501,751 Aldridge Mar. 28,` 1950 2,518,832 Stephens Aug. l5, 1950 2,631,614 Stephens Mar. 17, 1953 FOREIGN PATENTS 605,054 Great Britain July 15, 1948 

